NEXTMUSE - Deliverable D1.2 - Intermediate report on improvements of SPH method (numerical scheme, boundary treatment and multi-spatial resolution).

Following deliverable D1.1, in the present deliverable are reported the developments realized by the partners in the frame of the project regarding enhancement of the spatial accuracy and stability of the method, whilst minimising computational expense. The partners of the NextMUSE project share three of the most advanced and promising SPH formulations, a detailed comparison of which was given in the intermediate report D1.1, on their improvements and advancements. Investigations of corrected kernel techniques within the frame of Riemann-SPH variant is pursued and is reported in detail in Appendix C. In particular, it is studied the influence of these kernel corrections on the consistency of SPH with or without the presence of a boundary. It is especially looked at the influence of different parameters such as kernel support size, particle volumes and volume barycenters, or particle disorder. Finally, the improvement of the global SPH scheme including these corrected kernels is assessed on a number of test cases. Within this report, Incompressible SPH (ISPH) is also introduced as a fourth variant. This method was developed to address some of the problems associated with weakly compressible SPH, namely the stability of the pressure field and time step limitations. Recent developments in the Finite Volume Particle Method (FVPM) are then presented, aimed at reducing the computational expense of the method. Such developments include the implementation of a top-hat shaped particle weighting function, and square particle support domain. Efforts made on the treatment of boundaries are then described. To compliment the work presented in D1.1, further theoretical proof is given for the Normal Flux boundary method. A method to accurately treat inlet and outlet conditions within the FVPM framework is then presented. A variable resolution scheme is then described that includes the gradient of the smoothing length (?h terms) in the formulation. Such terms can be adapted to any SPH variant. The new scheme is then validated for hydrostatic and wedge impact tests, showing improved stability and properties of conservation. A description of an FVPM model that allows a smooth and continuous variation of particle size within a Eulerian framework is then given. The previously discussed ?h terms are then used to correct the kernel gradient in a variational SPH formulation, allowing regions (or blocks) of particles with large variations in h to interact in a stable way. Finally, a particle packing algorithm is presented that initialises particles in such a way to achieve static equilibrium, eliminating the generation of spurious currents caused by the re-settling of fluid particles. Such an initial configuration is of considerable advantage, particularly when modelling boundaries with frozen or fixed particles, and could be used dynamically to redistribute particles.